Re: Probabilistic polynomial time algorithm for solving the DLOG problem

On May 27, 2:59 am, Jeffrey Goldberg <nob...@xxxxxxxxxxxx> wrote:
On 11-05-26 9:22 PM, Jeffrey Goldberg wrote:

On 11-05-26 7:37 PM, Maaartin G wrote:
Using the hint that Pubkeybreaker gave that "Subgroups with size
5,7,8,9,10,11  are impossible" along with your example of even numbers
then a first guess is that [turned out to be wrong]

I'll play with this this evening.  Thanks!

I got stuck on the proof. The actual pattern is instantly clear.

For a Group {0, 1, ..., m-1} with a * b = a + b mod m, then for every n
such that n divides m there is a subgroup S_n containing all the
multiples of n mod m

Stop prattling and go READ.

The above statement is NOT TRUE. S_n has special meaning within
group theory. You would learn this if you bothered to do the
required
background reading.

You should also consider cases where m is prime, and where m is
odd.......


So in the case of m = 12 there are six subgroups including {0} and also
the not quite proper subgroup where n = 1, {0, 1, ..., 11}.

Do you know why all the sub-groups must contain 0????

that only those sets will be subgroups. Maybe I'll have to look up
Legrange's work after all. But I was hoping that I could prove this all
on my own.

Prove what on your own??? You have not stated a formal conjecture.
You should have STARTED by taking my hint and looking up Lagrange's
Thm. Look up "Sylow" as well.

READ.
.

Relevant Pages

  • Re: normal subgroups
    ... Rogério Brito wrote: ... could you give some hint on that: ... The first counterexample that came to my mind was Z with the subgroups 2Z and 3Z. ...
    (sci.math)
  • Re: normal subgroups
    ... could you give some hint on that: ... The first counterexample that came to my mind was Z with the subgroups 2Z and 3Z. ... Homepage on freshmeat: http://freshmeat.net/projects/algorithms/ ...
    (sci.math)
  • Re: sylow group
    ... I'm not sure my old hint means anything. ... Here's a fresh hint. ... that two sylow subgroups are conjugate. ...
    (sci.math)
  • Re: involutions of D4
    ... Hint: Consider how the involutions are embedded in the 3 ... subgroups of order 4. ... Jim Heckman ...
    (sci.math)
  • Recursive structure of Finite groups
    ... I'm going over my group theory book trying to recover all that I ... I know that groups have subgroups but I'm curious as to if any group ...
    (sci.math)